Fresh from winning the Europa League and securing Champions League qualification, attention has turned to summer reinforcements as Jose Mourinho's men look to challenge for the Premier League.
Press Association Sport understands United intend to make three or four high-quality additions this summer, but interest in Atletico Madrid's Griezmann has cooled.
The France international has long been linked with a move to Old Trafford, but the long-term injury sustained by top scorer Ibrahimovic means an out-and-out striker rather than a number 10 is their priority.
Ibrahimovic may not play again this year after sustaining serious knee ligament damage in the Europa League quarter-final second leg against Anderlecht in April.
The 35-year-old's contract at Old Trafford runs out this summer and his agent Mino Raiola admitted on Wednesday that he did not know where the Swede will be playing next season.
Another of Raiola's clients is Everton striker Romelu Lukaku.
United have been strongly linked with the player, who has two years left on his existing deal at Goodison Park and has refused to sign a new contract.
"Lukaku had a promise that if certain clubs came this summer that he could leave this summer," Raiola told talkSPORT.
"We are not in concrete talks with anybody at this moment, but hearing the market I think some clubs will contact Everton.
"If the price is right for Everton and the project is right for Lukaku then I think he will want to make another step, but we are not there yet."
Torino's Andrea Belotti and Alvaro Morata of Real Madrid are other strikers to have been linked with a summer move to Old Trafford, while speculation over fans' favourite Cristiano Ronaldo refuses to go away.
Also reported to be on United's radar are Inter Milan's Ivan Perisic, Burnley defender Michael Keane and Chelsea's Nemanja Matic.
